I mean if you had an entire team of them you could set them up pretty amazingly depending on what you were trying to deal with.

Swagger / Taunt / Substitute / Rest or Recover

Toxic / Pain Split / Purify / Bide

Swagger / Counter / Recover / Substitute

Reflect / Safeguard / Curse(or Harden I guess) / Baton Pass

Etc. etc.

It's not an ideal team insofar as you're going to really find some things suck to fight and will be exceptionally hard to deal with just based on the fact they'll have type advantage over you and even if over-levelled you're never really going to be faster than anything. But if you'd be willing to put up with that, and as long as you can probably have a friend get you the Pokemon you need then it's still, in theory, manageable.

I reckon it would only be fair to have a friend at least trade you one to two Pokemon, not super high level of course but at least half decent, mostly so that you have at least one Pokemon with a semi-stable moveset.

Otherwise you're already about 22-27 levels into the story by the time you start hitting them, unless you can get them earlier than I know about them. I also envision the use of items like Quick Claw depending on the set of moves, or things like Focus Band if you have a Counter-based one.

Yeah I like your idea of having at least one or two viable Pokemon outside of the Pyuks, I'm considering using my starter for that, at least at first. I might swap the starter out for something else later

Going to TRY five Pyuks for as long as possible though. If I start running into a common issue I'll pack something to counter it, I feel like especially strong electric or grass types will give me a lot of trouble [things like Ampharos that can take enough hits while also having high offensive stats] and whatever I do I need to make sure my rival isn't using Rowlet. Maybe I'll give him Popplio on purpose to make the types a bit more even... oh god his Pikachu/Raichu isn't going to be fun is it

Also this will be done on a vanilla Sun or Moon, not Ultra. I'll be breeding my Pyuks on another game & trading them as eggs near the start of the game, so they'll all have my own OT & won't disobey or grow too quickly. Thankfully since I upgraded to a 2ds xl I can trade with myself

And if I can complete this challenge I'll do an all-Wobbuffet challenge next.